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2012 Fiscal Year Final Research Report

Developments ofcomputational theory of real algebraic geometry for optimization problem

Research Project

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Project/Area Number 21340025
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyushu University

Principal Investigator

ANAI Hirokazu  九州大学, マス・フォア・インダストリ研究所, 教授 (20417520)

Co-Investigator(Kenkyū-buntansha) YOKOYAMA Kazuhiro  立教大学, 理学部, 教授 (30333454)
Co-Investigator(Renkei-kenkyūsha) YANAMI Hitoshi  富士通研究所, ソフトウェア技術研究所, 研究員 (70417533)
IWANE Hidenao  富士通研究所, ソフトウェア技術研究所, 研究員 (00470360)
Project Period (FY) 2009 – 2012
Keywords数式処理 / 最適化 / 数値 / 数式融合計算
Research Abstract

In this project we have developed effective and efficient quantifier elimination algorithms for optimization problems. We had many original results on quantifier elimination algorithms and published them in international academic journals. Moreover, we also published textbooks on quantifier elimination and optimization.

  • Research Products

    (37 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (13 results) (of which Peer Reviewed: 10 results) Presentation (19 results) Book (2 results) Remarks (3 results)

  • [Journal Article] An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination2013

    • Author(s)
      H. Iwane, H. Yanami, H. Anai, K. Yokoyama
    • Journal Title

      Theoretical Computer Science

      Volume: vol. 479 Pages: 43-69

  • [Journal Article] 自然言語処理と計算代数の接合による数学問題へのアプローチ(<特集>ロボットは東大に入れるか?)2012

    • Author(s)
      相澤 彰子, 松崎 拓也, 穴井 宏和
    • Journal Title

      人工知能学会誌

      Volume: 27(5) Pages: 483-491

    • Peer Reviewed
  • [Journal Article] 符号情報利用による数値数式 CAD の効率的な実装,(Computer Algebra : Design of Algorithms, Implementations and Applications2012

    • Author(s)
      岩根 秀直 , 穴井 宏和, 屋並 仁史
    • Journal Title

      数理解析研究所講究録

      Volume: 1815 Pages: 143-151

  • [Journal Article] Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries2012

    • Author(s)
      S.Orange, G.Renault, K.Yokoyama
    • Journal Title

      Mathematics in Computer Science

      Pages: 217-233

    • Peer Reviewed
  • [Journal Article] 数式処理に基づくパラメータ空間法によるロバスト制御系設計2011

    • Author(s)
      穴井宏和
    • Journal Title

      電気評論

      Volume: 2011 年 3月号 Pages: 15-18

  • [Journal Article] Optimizing a Particular Real Root of a Polynomial by a Special Cylindrical Algebraic Decomposition2011

    • Author(s)
      S. Gandy, M. Kanno, H. Anai, K.Yokoyama
    • Journal Title

      Mathematics in Computer Science

      Volume: 5(2) Pages: 209-221

    • Peer Reviewed
  • [Journal Article] An SOS-QE Approach to Nonlinear Gain Analysis for Polynomial Dynamical Systems2011

    • Author(s)
      H. Ichihara, H. Anai
    • Journal Title

      Mathematics in Computer Science

      Volume: 5(3) Pages: 303-314

    • Peer Reviewed
  • [Journal Article] A Symbolic-Numeric Approach to Multi-Objective Optimization in Manufacturing Design2011

    • Author(s)
      H. Iwane, H. Yanami, H. Anai
    • Journal Title

      Mathematics in Computer Science

      Volume: 5(3) Pages: 315-334

    • Peer Reviewed
  • [Journal Article] A Note on Distinct Nilpotency Decomposition of Polynomial Ideals over Finite Fields2010

    • Author(s)
      K. Yokoyama
    • Journal Title

      Commentarii Mathematici, niversitatis Sancti Pauli

      Volume: Vol. 59, No.2 Pages: 145-164

    • Peer Reviewed
  • [Journal Article] Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem2009

    • Author(s)
      H. Anai, S.Hara, M.Kannno, K.Yokoyama
    • Journal Title

      J. Symb. Comput

      Volume: 44(7) Pages: 703-725

    • Peer Reviewed
  • [Journal Article] Quintic Polynomials of Hashimoto-Tsunogai, Brumer and Kummer2009

    • Author(s)
      M. Kida, G Renoue, K. Yokoyama
    • Journal Title

      International Journal of Number Theory

      Volume: Vol. 5, No. 4 Pages: 555-571

    • Peer Reviewed
  • [Journal Article] Computer Algebra for Guaranteed Accuracy. How Does It Help?2009

    • Author(s)
      M.Kanno, H.Anai
    • Journal Title

      Japan J. Indust. Appl. Math

      Volume: Volume 26, Number 2 Pages: 517-530

    • Peer Reviewed
  • [Journal Article] Algebraic Approach to Discrete-time Polynomial Spectral Factorization, Journal of Math-for-Industry2009

    • Author(s)
      M. Kanno, K. Yokoyama, S. Hara, H. Anai
    • Journal Title

      Kyushu University

      Volume: Vol.1 JMI2009A-8 Pages: 57-68

    • Peer Reviewed
  • [Presentation] 代数幾何的アプローチによる多項式システムの解析2013

    • Author(s)
      穴井宏和
    • Organizer
      計測自動制御学会 第13回制御部門大会 特別企画「制御と数学が織り成す産業数学の展開」
    • Place of Presentation
      アクロス福岡
    • Year and Date
      2013-03-08
  • [Presentation] オークションメカニズムの多項式表現と限量記号消去法を用いたメカニズム設計の自動化2012

    • Author(s)
      杉町勇和, 岩崎敦, 横尾真, 穴井宏和
    • Organizer
      日本オペレーションズ・リサーチ学会秋季研究発表会
    • Year and Date
      2012-09-13
  • [Presentation] Usage of Modular Techniques for Efficient Computation of Ideal Operations2012

    • Author(s)
      K. Yokoyama
    • Organizer
      Computer Algebra in Scientific Computing CASC
    • Year and Date
      2012-09-04
  • [Presentation] 時間モデルを用いた並列性能予測の誤差を検討する方法2012

    • Author(s)
      折居茂夫, 穴井宏和
    • Organizer
      情報処理学会 第133回ハイパフォーマンスコンピューティング研究発表会
    • Place of Presentation
      有馬ビューホテルうらら
    • Year and Date
      2012-03-26
  • [Presentation] 信号処理への代数幾何的アプローチ,電子情報通信学会ソサイエティ大会企画セッション2011

    • Author(s)
      穴井宏和
    • Organizer
      信号処理工学の多様性と数理的体系化への挑戦
    • Place of Presentation
      北海道大学
    • Year and Date
      2011-09-13
  • [Presentation] Computational Real Algebraic Geometry and its Engineering Applications2011

    • Author(s)
      穴井宏和
    • Organizer
      日本学術振興会
    • Place of Presentation
      日本-欧州先端科学セミナー ESF-JSPS Frontier Science Conference for Young Researchers "Mathematics for Innovation: Large and Complex Systems"
    • Year and Date
      2011-03-01
  • [Presentation] On parametric optimization techniques for solving recursive formulas2011

    • Author(s)
      吉良知文, 岩根秀直, 穴井宏和
    • Organizer
      「不確実環境下での柔構造最適化モデリング」第7回研究会
    • Year and Date
      2011-01-29
  • [Presentation] 非線形ゲイン解析に対するSOS-QE アプローチ2011

    • Author(s)
      市原裕之, 穴井宏和
    • Organizer
      第11回 計測自動制御学会 制御部門大会
    • Year and Date
      2011-01-28
  • [Presentation] 代数的簡略化を用いたモデル予測制御の効率的方法2011

    • Author(s)
      梅田裕平, 丸山次人, 志村智洋, 穴井宏和
    • Organizer
      第11回 計測自動制御学会 制御部門大会
    • Year and Date
      2011-01-28
  • [Presentation] A symbolic-numeric approach to nonlinear dynamical system analysis2010

    • Author(s)
      H. Anai
    • Organizer
      SIAM / MSRI Workshop on Hybrid Methodologies for Symbolic-Numeric Computation
    • Year and Date
      2010-11-19
  • [Presentation] Computer Algebra - what does it bring to control system design?2010

    • Author(s)
      H. Anai
    • Organizer
      SICE Annual Conference 2010
    • Year and Date
      2010-08-19
  • [Presentation] CAD における i-projection operator 導入による QE の効率化2010

    • Author(s)
      岩根秀直, 穴井宏和, 屋並仁史
    • Organizer
      日本数式処理学会大会
    • Year and Date
      2010-06-12
  • [Presentation] A Symbolic-Numeric Approach to Multi-Parametric Programming for Control Design: ICROS-SIC2009

    • Author(s)
      H. Anai
    • Organizer
      International Joint Conference 2009
    • Year and Date
      2009-08-20
  • [Presentation] A Maple toolbox for parametric robust control system design using symbolic computation2009

    • Author(s)
      H. Noriko, H. Anai, S. Hara
    • Organizer
      ICROS-SICE international Joint Conference 2009
    • Year and Date
      2009-08-20
  • [Presentation] A Symbolic-Numeric Approach to Multi-Parametric Programming for Control Design: ICROS-SICE2009

    • Author(s)
      H. Anai
    • Organizer
      International Joint Conference 2009
    • Year and Date
      2009-08-20
  • [Presentation] An Effective Implementation of Symbolic-Nuneric Cylindrical Algebraic Decomposition for Quantifier Elimination2009

    • Author(s)
      H. Iwane, H. Yanami, H. Anai, K. Yokoyama
    • Organizer
      3rd International Workshop on Symbolic-Numeric Computation (SNC)
    • Year and Date
      2009-08-04
  • [Presentation] An Effective Implementation of Symbolic-Nuneric Cylindrical Algebraic Decomposition for Quantifier Elimination2009

    • Author(s)
      H. Iwane, H. Yanami, H. Anai, K. Yokoyama
    • Organizer
      3rd International Workshop on Symbolic-Numeric Computation (SNC) 2009
    • Year and Date
      2009-08-04
  • [Presentation] Plant/Controller Design Integration for H2 Control by Symbolic-Numeric Hybrid Optimization Based on Sum of Roots Characterization2009

    • Author(s)
      M. Kanno, S. Hara, H. Anai
    • Organizer
      3rd IEEE Multi-conference on Systems and Control (MSC2009)
    • Year and Date
      2009-07-09
  • [Presentation] Solution of Algebraic Riccati Equations Using the Sum of Roots2009

    • Author(s)
      M. Kanno, K. Yokoyama, H. Anai, S. Hara
    • Organizer
      International Symposium on Symbolic and Algebraic Computation (ISSAC) 2009
    • Year and Date
      2009-07-09
  • [Book] 数理最適化の実践ガイド2013

    • Author(s)
      穴井宏和
    • Total Pages
      160
    • Publisher
      講談社
  • [Book] QEの計算アルゴリズムとその応用-数式処理による最適化2011

    • Author(s)
      穴井宏和、横山和弘
    • Total Pages
      264
    • Publisher
      東京大学出版会
  • [Remarks] SyNRAC ダウンロードページ

    • URL

      http://jp.fujitsu.com/group/labs/techinfo/freeware/synrac/

  • [Remarks] 図書関連ホームページ

    • URL

      http://www.utp.or.jp/bd/978-4-13-061406-1.html

  • [Remarks]

    • URL

      http://www.kspub.co.jp/book/detail/1565104.html

URL: 

Published: 2014-08-29  

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